Results 271 to 280 of about 2,924,633 (320)

Nonlinear Approximation and (Deep) ReLU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {ReLU}$$\end{document}

Constructive approximation, 2019
This article is concerned with the approximation and expressive powers of deep neural networks. This is an active research area currently producing many interesting papers.
I. Daubechies, Ronald A. DeVore, S. Foucart, Boris Hanin, G. Petrova   +4 more
semanticscholar   +1 more source

Fuzzy-Approximation-Based Adaptive Output-Feedback Control for Uncertain Nonsmooth Nonlinear Systems

IEEE transactions on fuzzy systems, 2018
This paper proposes a solution to adaptive output-feedback control for a class of nonsmooth nonlinear systems. First, the concept of semiglobally uniformly ultimately bounded (SGUUB) stability that has been widely used for smooth nonlinear systems with ...
Xudong Zhao, Xinyong Wang, Guangdeng Zong, Hongmin Li   +3 more
semanticscholar   +1 more source

Nonlinear Approximation and Muckenhoupt Weights

Constructive Approximation, 2006
In the general atomic setting of an unconditional basis in a (quasi-) Banach space, we show that representing the spaces of m-terms approximation as Lorentz spaces is equivalent to the verification of two inequalities (Jackson and Bernstein), and that the validity of these two properties is equivalent to the Temlyakov property. The proof is very direct
Dominique Picard, Gerard Kerkyacharian, Gerard Kerkyacharian   +2 more
openaire   +4 more sources

Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation

arXiv.org
Accurate approximation of complex nonlinear functions is a fundamental challenge across many scientific and engineering domains. Traditional neural network architectures, such as Multi-Layer Perceptrons (MLPs), often struggle to efficiently capture ...
SS Sidharth, R. Gokul
semanticscholar   +1 more source

Two-Timescale Networks for Nonlinear Value Function Approximation

International Conference on Learning Representations, 2019
A key component for many reinforcement learning agents is to learn a value function, either for policy evaluation or control. Many of the algorithms for learning values, however, are designed for linear function approximation—with a fixed basis or fixed ...
Wesley Chung, Somjit Nath, A. Joseph, Martha White   +3 more
semanticscholar   +1 more source

Nonlinear Methods of Approximation [PDF]

Foundations of Computational Mathematics, 2003
Abstract. Our main interest in this paper is nonlinear approximation. The basic idea behind nonlinear approximation is that the elements used in the approximation do not come from a fixed linear space but are allowed to depend on the function being approximated.
openaire   +1 more source

Linear and Nonlinear Approximation

1996
Let f be a continuous function on the interval [a, b] ⊂ ℝ |R which is to be approximated by an approximation function Φ ∈ C[a, b]. Φ shall be dependent on x ∈ [a, b] and on certain parameters \( c_0 ,c_1 , \ldots ,c_n \):\( \Phi (x): = \Phi (x,c_0 ,c_1 , \ldots ,c_n ) = \Phi (x,c)\,for c = (c_0 ,c_1 , \ldots ,c_n )^T.
Gisela Engeln-Müllges, Frank Uhlig
openaire   +2 more sources

Nonlinear system approximations

26th IEEE Conference on Decision and Control, 1987
We are interested in approximating a nonlinear system by a feedback linearizable system instead of a linear system. Two approaches presently exist in the literature. One involves the concept of involutivity to a certain order, and the other considers a canonical expansion and pure feedback approximation.
Louis R. Hunt, Richard Goldthwait
openaire   +2 more sources

On the convex approximation of nonlinear inequalities

Optimization, 1974
The present paper deals with sufficient conditions for a system of convex incqualities to be a local approximation of a given arbitrary system in the following sense: the solution set of the first system is tangential to the solution set of the second one at the point under consideration. a criterion is proposed. For the case, in which the given system
openaire   +3 more sources

Analytical approximation of nonlinear distortions

IEEE Photonics Technology Letters, 2005
We present an analytical approximation that can describe the signal at the output of a nonlinear fiber, accounting for the distortions induced by the interplay between chromatic dispersion and Kerr nonlinearity. The obtained results agree well with the split-step Fourier method for launch powers as high as 10 dBm.
CIARAMELLA, ERNESTO, FORESTIERI, Enrico
openaire   +3 more sources